Problem: Jessica is 3 times as old as Michael. Twenty years ago, Jessica was 7 times as old as Michael. How old is Michael now?
Solution: We can use the given information to write down two equations that describe the ages of Jessica and Michael. Let Jessica's current age be $j$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $j = 3m$ Twenty years ago, Jessica was $j - 20$ years old, and Michael was $m - 20$ years old. The information in the second sentence can be expressed in the following equation: $j - 20 = 7(m - 20)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to use our first equation for $j$ and substitute it into our second equation. Our first equation is: $j = 3m$ . Substituting this into our second equation, we get: $3m$ $-$ $20 = 7(m - 20)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $3 m - 20 = 7 m - 140$ Solving for $m$ , we get: $4 m = 120.$ $m = 30$.